if someone walks 1.5 km west then 2.5 km 30 degrees south of east then 1.5 km 40 degrees north of east. Starting at the same point, what would be the angle to get someone straight from the starting point to where the other person ended??
break up each part of the trip into N,E components then add.
-1.5E+2.5Sin30E-2.5cos30N+1.5sin40N+1.5cos30E=final
then, after adding the N, and E components...
theta=arctan=Ncomponents/Ecomponents
To find the angle to get someone straight from the starting point to where the other person ended, we need to determine the final displacement of the second person.
Let's break down the movements of the second person step by step:
1. The person walks 1.5 km west. This means they move directly opposite to the east direction.
2. Then, the person walks 2.5 km 30 degrees south of east. This means they move in the southeast direction (south-eastwards) by an angle of 30 degrees with respect to the east direction.
3. Finally, the person walks 1.5 km 40 degrees north of east. This means they move in the northeast direction (north-eastwards) by an angle of 40 degrees with respect to the east direction.
To find the overall displacement, we can represent these three movements as vectors and add them up. We'll use a coordinate system where east is the positive x-axis and north is the positive y-axis.
1. The first movement of walking 1.5 km west can be represented as a vector (-1.5, 0) since it moves only in the negative x-axis direction.
2. The second movement of walking 2.5 km 30 degrees south of east can be split into its east and south components. The south component can be found by multiplying the hypotenuse (2.5 km) by the sine of the angle (30 degrees), giving us 2.5 * sin(30) = 1.25 km. The east component can be found by multiplying the hypotenuse (2.5 km) by the cosine of the angle (30 degrees), giving us 2.5 * cos(30) = 2.165 km. Thus, the second movement can be represented as a vector (2.165, -1.25).
3. Similarly, the third movement of walking 1.5 km 40 degrees north of east can be split into its east and north components. The north component can be found by multiplying the hypotenuse (1.5 km) by the sine of the angle (40 degrees), giving us 1.5 * sin(40) = 0.9659 km. The east component can be found by multiplying the hypotenuse (1.5 km) by the cosine of the angle (40 degrees), giving us 1.5 * cos(40) = 1.147 km. Thus, the third movement can be represented as a vector (1.147, 0.9659).
To find the overall displacement, we can add up the three vectors:
(-1.5, 0) + (2.165, -1.25) + (1.147, 0.9659) = (1.812, -0.2841)
The overall displacement vector is (1.812, -0.2841), which means the person ended up 1.812 km east and 0.2841 km south of the starting point.
To find the angle between the starting point and the end point, we can use the inverse tangent function (arctan) with the y-component divided by the x-component:
Angle = arctan(-0.2841 / 1.812) ≈ -8.913 degrees
Therefore, the angle to get someone straight from the starting point to where the other person ended is approximately -8.913 degrees.